This equal-growth, degenerate solution is seen in Fig.(REF ) by following the blue-solid line passing through the origin. It intersects the circle at \(\sqrt{2}\)  indicated by the small blue rectangle. Every point on this line represents \(\kappa _1=\kappa _2\)  with growth \(\delta _1=\delta _2\) . Hence, when \(\kappa _1 \rightarrow \kappa _2=\kappa \) , following l'Hôspital's rule, it becomes the degenerate breather solution. With \(\kappa \rightarrow 0\) , following the blue line to the origin, the solution becomes a second-order rational solution. Both of these solutions have been studied and presented in [1]}, [2]}.
